An Urban Search and Rescue officer from London Fire Brigade inside the Grenfell Tower in west London after a fire engulfed the 24-storey building on Wednesday morning, Saturday, June 17, 2017. Public Credit: David Mirzoeff/AP

If that death toll is confirmed, it would make the Grenfell Tower blaze the deadliest in London since World War Two.

"Sadly at this time, there are 58 people who we have been told were in Grenfell Tower on the night that are missing and therefore sadly I have to assume that they are dead," Commander Stuart Cundy told reporters.

Cundy added that the figure could change. Police had previously put the death toll at 30.

"The figure of 30 that I gave yesterday is the number that I know, sadly, have, at least, died. So that 58 would include that 30," he said.

Prime Minister Theresa May's government earlier sought to quell anger over the fire, pledging to support the victims of the blaze after protesters jeered her when she visited local residents.

May was rushed away from a meeting with residents on Friday under heavy police guard as protesters shouted "Shame on you" and hundreds stormed a local town hall calling for justice.

After a botched snap election that lost her party its majority in parliament, May is facing criticism for her response to the blaze which engulfed the 24-storey apartment block of social housing on Wednesday.

Residents of the destroyed tower said May was far too slow to visit the stricken community, that the building had been unsafe and that officials have failed to give enough information and support to those who have lost relatives and their homes.

Asked repeatedly whether she had misread the public mood, May did not answer directly but said the focus was on providing support to the victims."What I'm now absolutely focused on is ensuring that we get that support on the ground," May said in a BBC Newsnight interview.

"Government is making money available, we're ensuring that we're going to get to the bottom of what's happened, we will ensure that people are rehoused. But we need to make sure that that actually happens."

May on Saturday chaired a meeting on the government's response to the fire. She also met victims of the fire in Downing Street.

Alongside both police and fire investigations into the blaze, she has promised to set up a public inquiry.

She also pledged 5 million pounds ($6.39 million) of support, housing guarantees and help with access to bank accounts and cash. Those who lost their homes will be rehoused within three weeks, she said.

One of her closest allies, Damian Green, defended May on Saturday, adding that a team would go to the area to answer questions from residents.

"The Prime Minister is distraught about what has happened," said Green, who was appointed May's deputy in the wake of the general election.

"We're all desperately sad, we're all angry, but of course none of us as angry as those who were directly affected. I absolutely get why they're angry," Green said.